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Who are Thing One and Thing Two in The Cat in the Hat?

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In the classic children's book The Cat in the Hat, Thing One and Thing Two are two small, blue-haired creatures that the Cat releases from a large red box to entertain the two bored siblings. Although the Cat describes them as "tame," they prove to be unruly, flying kites through the house and causing a significant mess before the boy eventually catches them with a net.1